The PDE framework Peano applied to fluid dynamics: an efficient implementation of a parallel multiscale fluid dynamics solver on octree-like adaptive Cartesian grids (original) (raw)
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32nd Aerospace Sciences Meeting and Exhibit
A breakthrough in computer performance is possible, as has been demonstrated in the last years [I], by using the massively parallel machines 121. Massively parallel computers use very large number of processors operating simultaneously in either SIMD (Single Instruction Multiple Data), MIMD (Multiple Instruction Multiple Data) or a combination of the two. The availability of massively parallel machines in the market created a need for software which is capable of taking advantage of the new technology. Several problems arise when an efficient implementation on a massively parallel machine is sought. The most time consuming part of a massively parallel computation is the interprocessor communication rather than floating point operations [3]. An effort must be directed, thus, to more efficient communication. An efficient treatment of boundary conditions is mandatory in massively parallel applications. Typically only a small portion of the 4
Parallel Computing on the Navier-Stokes Solver with the Multigrid Method
This paper is aimed to present the combination of the parallel computing and the multigrid method on the Navier-Stokes solver. The combination is based on the concept of the object-oriented programming (OOP), which consists of 4 independent modules: Grid Generation, Navier-Stokes Solver, Multigrid Method and Parallel Computing modules. The multigrid method is implemented by employing the full approximation storage (FAS) scheme for numerically solving the non-linear Navier-Stokes equations. The overall computation is performed by using the parallel computing in which a number of computers are concurrently computed for the same task but on different subdata. The two-dimensional laminar flow in a cavity at Re=1,000 is used as a test case. It is found that the computational time is decreased significantly when employing the combination of the multigrid method and the parallel computing.
MPI-Parallelization of a Structured Grid CFD Solver including an Integrated Octree Grid Generator
An existing Computational Fluid Dynamics (CFD) solver is parallelized by means of MPI. The solver includes a dynamic and adaptive grid generator for Cartesian Quadtree and Octree grids, which therefore also have to be parallelized. The grid generator generates grids fulfilling a specific set of rules, that have to be enforced also in parallel. The assembly of the large sparse matrices resulting from the implicit discretization of Navier-Stokes equations is done in parallel, as is the solving process. The parallel performance of both of these processes depends heavily on a good load balancing in order to reach satisfactory speedup. Two versions of load balancing are demonstrated, one based on block swapping, and the other by utilizing the Metis or Parmetis software packages for load balancing of graphs. Results are presented for load balancing and for the parallel speedup of solving the linear algebra system of equations.
Distributed parallel processing applied to an implicit multigrid Euler/Navier-Stokes algorithm
31st Aerospace Sciences Meeting, 1993
An implicit multigrid algorithm for the solution of the Euler and Navier-Stokes Equations has been implemented within the framework of multiple blockstructured grids in which the physical domain is spatially decomposed into several blodrs and the solution is advanced in parallel on each block. Utilities have been developed to implement such a scheme in a d i e tributed computing environment. The multi-block algorithm is designed so that the explicit residual calculation is identical to that of the single-block scheme, and therefore converged solutions for both schemes must be the same. To accelerate convergence, synchronous and asynchronous multigrid strategies are implemented. Significant speedups have been achieved in a multiple processor environment, while convergence rates similar to those of the singleblock scheme are observed. With the recent advances in computer architecturespecifically the availability of low-cost high-speed cornputer workstations, the development of multiple prople processor IBM ES/3090 6OOJ supercomputer us-*ReMarch Scientist. Member AIAA. 'Professor, Sibley School of Mechanicaland Aerospace En& '%a' neering. Associate Fellow AIAA. Copyright A~~, +~~ h t i t u l e of Aeranautics and Astronsutics, Inc. AU rights merved.
Asynchronous Navier-Stokes Solver on 3D Unstructured Grids for the Exascale Era
2019
This project has developed multiple fluid dynamics solvers for complex 3D flows using fully asynchronous distributed-memory task-parallel algorithms on top of the Charm++ [1] runtime system. The algorithms solve the Euler or Navier-Stokes equations of compressible flows using unstructured tetrahedron meshes with optional solution-adaptive mesh-, and polynomial-order refinement. We have demonstrated excellent strong scaling up 50K compute cores and the benefits of Charm++'s automatic load balancing. 2 Accomplishments at a glance • Implemented the first unstructured-mesh partial differential equations (PDE) solver on the Charm++ runtime system with automatic load balancing. • Demonstrated, for the first time, that excellent parallel performance can be achieved using Charm++ of a PDE solver on unstructured grids, useful for complex 3D engineering problem geometries. • Implemented both node-centered and cell-centered finite element algorithms for the simulation of compressible high-speed flows. All algorithms are in 3D, fully asynchronous, task-based, distributedmemory-parallel, and exhibit excellent strong scaling up to 50K CPU cores, the most tested. • Developed and implemented a new adaptive DG algorithm that automatically adjusts the order of the approximation polynomial based on local error estimators and exercised it for single-material verification cases on 3D unstructured meshes with Charm++'s automatic load balancing capabilities. • Developed, implemented, and verified a new DG method for compressible multi-material flows. • Implemented adaptive mesh refinement in 3D using an, asynchronous distributed-memory-, taskparallel algorithm. • Developed the code in a production fashion, with extensive unit-, and regression test suites and highdegree of code reuse using the C++17 standard. Also exercise mandatory code reviews, test code coverage analysis, using LANL-internal and public-facing continuous integration servers. • Implemented various code capabilities that enable large-scale fluid dynamics, e.g., file/rank N-to-M parallel I/O, checkpoint/restart, and compile-time-configurable zero-runtime-overhead memory layout for large-data arrays to enable enable performance-portability across different architectures. • Released the code as open source, see https://quinoacomputing.org.
This paper aims at coupling two known CFD techniques, namely multigrid and parallelization, in an existing Euler equations solver for 2D and 3D unstructured grids. The solver is based on a time-marching formulation for the high-subsonic/transonic flow equations and a pointwise implicit solution algorithm. The gain from the combined use of multigrid and parallelization is the reduction of both CPU cost and elapsed computational time associated with the use of the aforementioned software. Multigrid is employed using a finite-volume agglomeration algorithm without explicitly defining coarser grids, the latter being a common practice in structured grids' multigrid. Parallelization relies on the concurrent processing of grid subsets on a cluster of networked processors. The unstructured grid is partitioned through a genetic algorithm based tool which yields equal load per processor and minimal inter-processor communication of data during the iterative scheme. The computational gain i...
A Solution Adaptive Multi-Grid Euler Solver on Two-Dimensional Cartesian Grids
2015
Cartesian grid method for inviscid flows was a very popular and powerful tool in late 80’s for its robustness, quick solution convergence and automatic grid adaption around complex geometries. In last decade, by the help of ingenious approaches and fast computers, the method is born out of its ashes. In this paper, it is aimed to generate locally refined hierarchical Cartesian grids for twodimensional irregular geometries to provide solutions, which are easy to realize and accurate in the case of inviscid compressible flows around such geometries. Automatic Cartesian grid generation methodology is implemented in object-oriented FORTRAN programming language. Dynamic quadtree data structure algorithm is used to store the parent/child and cell/neighbor connectivities. The grid typically begins with a single root cell, and grows by a recursive subdivision of each cell into its four children which is done in coarsening part of the FORTRAN 90 subroutines. The goals are to enhance automati...
12th Computational Fluid Dynamics Conference, 1995
This paper presents a finite volume cell-centered technique for computing steady state solutions of the full Euler and Navier-Stokes equations on unstructured meshes. We aim t o design a scheme which is the most possible insensitive t o grid distortions, while however remaining of practical interest in terms of CPU time, storage and convergence. For that purpose, we use an original quadratic reconstruction with a fixed stencil and a high order flux integration by the Gauss quadrature rule t o compute the advective term of the equations. Time evolution is presently performed with an explicit multi-step Runge-Kutta scheme. A very general adaptation procedure based on h-refinement and coarsening is employed t o improve the resolution of complex flow features. The accuracy of the method is demonstrated for a linear equation and for inviscid and viscous flow computations. The inviscid flow over the NACA0012 airfoil is computed at various Mach numbers. These calculations illustrate the effectiveness of the adaptation procedure. We investigate the supersonic flow over a compression ramp t o validate the Navier-Stokes solver by using a hybrid grid.
A space-time parallel algorithm with adaptive mesh refinement for computational fluid dynamics
Computing and Visualization in Science, 2020
This paper describes a space-time parallel algorithm with space-time adaptive mesh refinement (AMR). AMR with subcycling is added to multigrid reduction-in-time (MGRIT) in order to provide solution efficient adaptive grids with a reduction in work performed on coarser grids. This algorithm is achieved by integrating two software libraries: XBraid (Parallel time integration with multigrid. https://computation.llnl.gov/projects/parallel-timeintegration-multigrid) and Chombo (Chombo software package for AMR applications-design document, 2014). The former is a parallel time integration library using multigrid and the latter is a massively parallel structured AMR library. Employing this adaptive space-time parallel algorithm is Chord (Comput Fluids 123:202-217, 2015), a computational fluid dynamics (CFD) application code for solving compressible fluid dynamics problems. For the same solution accuracy, speedups are demonstrated from the use of space-time parallelization over the time-sequential integration on Couette flow and Stokes' second problem. On a transient Couette flow case, at least a 1.5× speedup is achieved, and with a time periodic problem, a speedup of up to 13.7× over the time-sequential case is obtained. In both cases, the speedup is achieved by adding processors and exploring additional parallelization in time. The numerical experiments show the algorithm is promising for CFD applications that can take advantage of the time parallelism. Future work will focus on improving the parallel performance and providing more tests with complex fluid dynamics to demonstrate the full potential of the algorithm. Keywords Time-parallel • Mesh parallel-in-time • Adaptivity • Multigrid • MGRIT • High-order CFD • Finite-volume Communicated by Robert Speck.
An approach to optimizing adaptive parabolic PDE solvers for the Grid
Proceedings International Parallel and Distributed Processing Symposium
The Method of Lines is a widely used algorithm for solving parabolic partial differential equations that could benefit greatly from implementation on Grid computing environments. This work outlines the issues involved in executing Method-of-Lines codes on a Grid and in developing model-driven adaptive control strategies for these codes. We have developed a parameterizable benchmark called MOL that captures a wide range of realistic Method-of-Lines codes. We are using this benchmark to develop performance models that can be used to achieve specific optimality criteria under the available (and dynamically varying) resources of a Grid environment, and under user-specified goals for solution error and computational rate-ofprogress. We are developing a componentization strategy that can enable effective adaptive control of MOL, as well as language and compiler support that can simplify the development of adaptive distributed applications. If successful, this work should yield a much better understanding than we have at present of how an important class of parallel numerical applications can be executed effectively in a dynamic Grid environment.